Math Problem Statement

y=3x−2: Draw a graph of the equation on a coordinate plane. Label your axes, choose an appropriate scale, and plot at least three points.

Solution

import matplotlib.pyplot as plt import numpy as np

Define the function y = 3x - 2

def linear_function(x): return 3 * x - 2

Generate x values and calculate corresponding y values

x_values = np.linspace(-2, 3, 100) # Choose a range for x to cover more of the graph y_values = linear_function(x_values)

Plot the graph

plt.figure(figsize=(8, 6)) plt.plot(x_values, y_values, label="y = 3x - 2", color="blue")

Plot at least three specific points

specific_points_x = [-1, 0, 2] specific_points_y = [linear_function(x) for x in specific_points_x] plt.scatter(specific_points_x, specific_points_y, color="red")

Label these points

for (x, y) in zip(specific_points_x, specific_points_y): plt.text(x, y, f"({x},{y})", fontsize=9, ha='right')

Label axes and add title

plt.xlabel("x-axis") plt.ylabel("y-axis") plt.title("Graph of y = 3x - 2") plt.axhline(0, color='black',linewidth=0.5) plt.axvline(0, color='black',linewidth=0.5) plt.grid(True) plt.legend()

plt.show() <<ImageDisplayed>>successHere is the graph of the equation y=3x2y = 3x - 2. The axes are labeled, and I’ve selected a scale to capture the line clearly. The graph includes three specific points: (1,5)(-1, -5), (0,2)(0, -2), and (2,4)(2, 4), which are plotted and labeled on the coordinate plane.

Would you like additional details or have any questions?

Here are related questions for further exploration:

  1. How would the graph change if the slope were altered to 2 instead of 3?
  2. What would happen if we changed the y-intercept to 1 instead of -2?
  3. How can you determine the x-intercept of this line algebraically?
  4. How would you find the distance between two points on this line?
  5. What is the significance of the slope in real-world applications?

Tip: The slope, 3, indicates how steeply the line rises as x increases—specifically, for each unit increase in x, y increases by 3 units.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry
Slope-Intercept Form

Formulas

y = mx + b

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 6-8